What are quadratic equations and how do I solve them?

What are quadratic equations and how do I solve them?

Quadratic equations are polynomial equations of the form ax² + bx + c = 0. You can solve them using factoring, completing the square, or the quadratic formula.

Can you explain the quadratic formula?

Sure! The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). It gives the solutions for any quadratic equation.

What does the discriminant tell us?

The discriminant, b² - 4ac, indicates the nature of the roots. If it's positive, there are two real solutions; if zero, one real solution; and if negative, no real solutions.

Can you show me an example of solving a quadratic equation?

Of course! Let's solve x² - 5x + 6 = 0. Factoring gives us (x - 2)(x - 3) = 0, so x = 2 and x = 3.